A mathematical model of the mechanical subsystem of the trailer brake axle is described, which consists of a brake actuator, an application device and a drum brake. In the differential equation of motion, the total force from the mechanical subsystem reduced to the piston is described with a two-range linear-exponential model. The parameters of this model were determined using numerical identification, based on experimental, quasi-static curves of pressure in the air brake chamber as a function of pushrod displacement. An example of use of the mechanical subsystem mathematical model to simulate the dynamics of a single-axle agricultural trailer's dual-line braking system with the Matlab-Simulink software is provided. The obtained results confirmed that the developed model is useful for testing transient processes in the air braking systems of tractor and truck trailers. The proposed experimental force curve determination method can also be used in the diagnostics of brake adjustment.